Bayesian Methods for Data AnalysisBroadening its scope to nonstatisticians, Bayesian Methods for Data Analysis, Third Edition provides an accessible introduction to the foundations and applications of Bayesian analysis. Along with a complete reorganization of the material, this edition concentrates more on hierarchical Bayesian modeling as implemented via Markov chain Monte Carlo ( |
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Page 29
... median of θ with a question like Can you determine a value (your median) such that θ is equally likely to be less than or greater than this point? and then follow up with a question about the 25th percentile, say Suppose you were told ...
... median of θ with a question like Can you determine a value (your median) such that θ is equally likely to be less than or greater than this point? and then follow up with a question about the 25th percentile, say Suppose you were told ...
Page 39
... median parameters. Berger (1985, pp.83–84) shows that, for a prior on θ to be invariant under location transformations (i.e., transformations of the form Y = X + c), it must be uniform over the range of θ. Hence the noninformative prior ...
... median parameters. Berger (1985, pp.83–84) shows that, for a prior on θ to be invariant under location transformations (i.e., transformations of the form Y = X + c), it must be uniform over the range of θ. Hence the noninformative prior ...
Page 41
... median, or mode. In principle, the mode is the easiest to compute, since no standardization of the posterior is then required; we may work directly with the numerator of (2.1). Also, note that when the prior π(θ) is flat, the posterior ...
... median, or mode. In principle, the mode is the easiest to compute, since no standardization of the posterior is then required; we may work directly with the numerator of (2.1). Also, note that when the prior π(θ) is flat, the posterior ...
Page 42
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Page 43
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Contents
| 1 | |
| 15 | |
CHAPTER 3 Bayesian computation | 105 |
CHAPTER 4 Model criticism and selection | 167 |
CHAPTER 5 The empirical Bayes approach | 225 |
CHAPTER 6 Bayesian design | 269 |
CHAPTER 7 Special methods and models | 311 |
CHAPTER 8 Case studies | 373 |
APPENDIX A Distributional catalog | 419 |
APPENDIX B Decision theory | 429 |
APPENDIX C Answers to selected exercises | 445 |
References | 487 |
Back cover | 521 |
Other editions - View all
Bayesian Methods for Data Analysis, Third Edition Bradley P. Carlin,Thomas A. Louis No preview available - 2008 |
Common terms and phrases
approximation assume baseline Bayes factor Bayes rule Bayesian approach Bayesian model beta BUGS code Carlin chain closed form components compute conditional distributions conjugate prior consider convergence covariate credible interval dataset empirical Bayes equation error evaluation example Figure frequentist full conditional distributions gamma Gaussian Gelfand Gibbs sampler given histogram hyperprior indifference zone interval iteration Jeffreys prior joint posterior likelihood loss function LVAD1 LVAD2 marginal distribution marginal likelihood marginal posterior matrix MCMC median methods Metropolis-Hastings algorithm Monte Carlo multivariate normal NPML observed data obtain optimal p-value parameter space patients percentiles plot point estimate posterior density posterior distribution posterior mean posterior probability prior distribution prior mean probability problem produce random effects regression risk sample sigma simulation specification statistical Subsection Suppose Table tion treatment univariate values variable variance vector WinBUGS